Mean and Median
ICSE · Class 9 · Mathematics
Quick revision notes for Mean and Median — ICSE Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Mean of Ungrouped Data
- Mean is the arithmetic average of all observations in a dataset
- Also called arithmetic mean or simply average
- Formula: x̄ = (Sum of all observations) ÷ (Number of observations)
Properties of Mean
- Property 1: Sum of deviations from mean equals zero ∑(x - x̄) = 0
- Property 2: If each observation increases by 'a', mean increases by 'a'
- Property 3: If each observation decreases by 'a', mean decreases by 'a'
Correcting Errors in Mean Calculation
- When observations are recorded incorrectly, mean needs correction
- Formula: Correct mean = (Incorrect sum - wrong value + correct value) ÷ n
- First find incorrect sum using: Incorrect sum = Incorrect mean × n
Combined Means and Grouped Data
- When combining groups with different means, use weighted average
- Formula: Combined mean = (n₁x̄₁ + n₂x̄₂) ÷ (n₁ + n₂)
- Each group's contribution depends on both its size and mean
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